Abstract




 
   

IJE TRANSACTIONS B: Applications Vol. 19, No. 1 (December 2006) 61-72   

downloaded Downloaded: 113   viewed Viewed: 1811

  THREE DIMENSIONAL ANALYSIS OF LAMINATED CYLINDRICAL PANELS WITH PIEZOELECTRIC LAYERS
 
A. Nosier and M. Ruhi*

Department of Mechanical Engineering, Sharif University of Technology
Tehran, Iran
Nosier@sharif.edu - Mohammad_Ruhi@yahoo.com

*Corresponding Author

 
( Received: November 18, 2004 – Accepted in Revised Form: June 01, 2006 )
 
 

Abstract    A semi-analytical solution is presented for three dimensional elastic analysis of finitelylong, simply supported, orthotropic, laminated cylindrical panels with piezoelectric layers subjected to outer pressure and electrostatic excitation. Both the direct and inverse piezoelectric effects are investigated. The solution is obtained through reducing the highly coupled partial differential equations (PDE's) of equilibrium to ordinary differential equations (ODE's) with variable coefficients by means of trigonometric function expansion in longitudinal and circumferential directions. The resulting ODE's are solved by dividing the radial domain into some finite subdivisions and imposing necessary continuity conditions between the adjacent sub-layers. Some numerical examples are presented for the stress distribution and electric responses due to outer pressure in both sensorial and actuating states. Also, the effect of geometric properties on the sensitivity and actuating power of the structure are investigated.

 

Keywords    Piezoelectric, Laminated Cylindrical Panel, Finite, Analytical

 

References   

 
1. Tauchert, T. R., “Plane Piezothermoelastic Response of a Hybrid Laminate-A Benchmark Problem”, Composite Structures, Vol. 39, (1997), 329-336.

2. Ding, H. J. and Chen, W. Q., “Three Dimensional Problems of Piezoelasticity”, New York, Nova Science Publishers, (2001).

3. Chen, S., Soh, A. K., Long, Y. Q. and Yao, Z. H., A., “New 4-Node Quadrilateral FE Model with Variable Electrical Degree of Freedom for the Analysis of Piezoelectric Laminated Composite Plates”, Composite Structures, Vol. 58, (2002), 583-599.

4. Altay, G. A., and Dokmeci, M. C., “Some Comments on the Higher Order Theories of Piezoelectric, Piezothermoelastic and Thermopiezoelectric Rods and Shells”, Int. J. Solids Struct., Vol. 40, (2003), 4699-4706.

5. Mannini, A. and Gaudenzi, P., “Multi-Layer Higher-Order Finite Elements for the Analysis of Free-Edge Stresses in Piezoelectric Actuated Laminates”, Composite Structures, Vol. 61, (2003), 271-278.

6. Mitchell, J. A. and Reddy, A., “Study of Embedded Piezoelectric Layers in Composite Cylinders”, J. Appl. Mech., Vol. 62, (1995), 166-173.

7. Chen, C. Q. and Shen, Y. P., “Piezothermoelasticity Analysis for a Circular Cylindrical Shell under the State of Axisymmetric Deformation”, Int. J. Eng. Sci., Vol. 34, No. 14, (1996), 1585-1600.

8. Chen, C. Q., Shen, Y. P., Liang, X., “Three-Dimensional Analysis of Piezoelectric Circular
Cylindrical Shell of Finite Length”, Acta Mech., Vol. 134, (1999), 235-249.

9. Chen, C. Q., Shen, Y. P., Wang, X. M., “Exact Solution of Orthotropic Cylindrical Shell with Piezoelectric Layers Under Cylindrical Bending”, Int. J. Solid Structures, Vol. 33, (1996), 4481-4494.

10. Wu, X. H., Chen, C. Q., Shen, Y. P., and Tian, X. G., A Higher-Order Theory for Functionally Graded Piezoelectric Shells, Int. J. Solids Struct., Vol.39, No.20, (2002), 5325-5344.

11. Wang, X. and Zhong, Z., “A Finitely Long Circular Cylindrical Shell of Piezoelectric/Piezomagnetic Composite under Pressuring and Temperature Change”, Int. J Eng. Sci., Vol. 41, (2003), 2429-2445.

12. Kapuria, S., Dumir, P. C. and Sengupta, S., “Exact Piezothermoelastic Axisymmetric Solution of a Finite Transversely Isotropic Cylindrical Shell”, Computers and Structures, Vol. 61, No. 6, (January 1996), 1085-1099.

13. Ossadzow, C. and Touratier, M., “A Multilayered Piezoelectric Shell Theory”, Composites Science and Technology, (2004), [in press].

14. Wu, X. H., Shen, Y. P. and Chen, C., “An Exact Solution for Functionally Graded Piezothermoelastic Cylindrical Shell as Sensors or Actuators”, Materials Letters, Vol. 57, (2003), 3532-3542.

15. Ma, L. F., Chen, Y. H. and Zhang, S. Y., “On the Explicit Formulations of Circular Tube, Bar and Shell of Cylindrically Piezoelectric Material Under Pressuring Load”, Int. J. of Eng. Sci., Vol. 39, (2001), 369-385.

16. Ashida, F., “Reduction of Applied Electric Potential Controlling Thermoelastic Displacement in a Piezoelectric Actuator”, Arch. Appl. Mech., Vol. 69, (1999), 443-454.

17. Kapuria, S., Sengupta, S. and Dumir, P. C., “Three-Dimensional Piezothermoelastic Solution for Shape Control of Cylindrical Panel”, J. Thermal Stresses, Vol. 20, (1997), 67-85.

18. Ashida, F. and Tauchert, T. R., “Control of Transient Thermoelastic Displacement in a Composite Disk”, J. Thermal Stresses, Vol. 25, (2002), 99-121.

19. Ootao, Y. and Tanigawa, Y., “Control of Transient Thermoelastic Displacement of an Angle-Ply Laminated Cylindrical Panel Bonded to a Piezoelectric Layer”, Appl. Math. and Computations, Vol. 148, (2004), 263-286.

20. Tzou, H. S., “Piezoelectric Shells: Distributed Sensing and Control of Continua”, Kluwer Acad. Pub., Boston/Dordrecht, (1993).

21. Tiersten, H. F., “Linear Piezoelectric Plate Vibrations”, Plenum Press, New York, (1969).

22. Rogacheva, N. N., “The Theory of Piezoelectric Shells and Plates”, CRC Press, (1994).

23. Xu, K. and Noor A. K., “Three-Dimensional Analytical Solutions for Coupled Thermoelectroelastic Response of Multilayered Cylindrical Shells”, AIAA J., Vol. 34, No. 4, (1996), 802-812.

24. Reddy, J. N., “On Laminated Composite Plates with Integrated Sensors and Actuators”, Engineering Structures, Vol. 21, (1999), 568-593.

25. Tauchert, T. R., Ashida, F., Noda, N., Adali, S. and Verijenko, V., “Developments in Thermopiezoelasticity with Relevance to Smart Composite Structures”, Composite Structures, Vol. 48, (2000), 31-38.

26. Giacovazzo, C., Monaco, H. L., Artioli, G., Viterbo, D. and Ferraris, G., “Fundamentals of Crystallography”, Oxford Science Pub., (1992).

27. Nye, N. Y., “Physical Properties of Crystals”, Oxford University Press, (1972).

28. Cady, W. G., “Piezoelectricity”, Dover Pub., New York, (1964).

29. Ikeda, T., “Fundamentals of Piezoelectricity”, Oxford University, (1990).

30. Herakovich, C. T., “Mechanics of Fibrous Composites”, John Wiley and Sons, Inc., (1998).





International Journal of Engineering
E-mail: office@ije.ir
Web Site: http://www.ije.ir